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          java二分查找
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        <h4 id="二分查找的原理"><a href="#二分查找的原理" class="headerlink" title="二分查找的原理"></a>二分查找的原理</h4><p>要求：必须要有一个有序的列表。如果没有的话，可以先使用排序算法进行排序。</p>
<blockquote>
<p>以升序数列为例，比较一个元素与数列中的中间位置的元素的大小，如果比中间位置的元素大，则继续在后半部分的数列中进行二分查找；如果比中间位置的元素小，则在数列的前半部分进行比较；如果相等，则找到了元素的位置。每次比较的数列长度都会是之前数列的一半，直到找到相等元素的位置或者最终没有找到要找的元素。</p>
</blockquote>
<span id="more"></span>
<h5 id="一个栗子"><a href="#一个栗子" class="headerlink" title="一个栗子"></a>一个栗子</h5><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">public</span> <span class="keyword">class</span> <span class="title class_">BinarySearch</span> &#123;</span><br><span class="line">    <span class="keyword">private</span> <span class="type">int</span>[] array;</span><br><span class="line">    <span class="comment">/**</span></span><br><span class="line"><span class="comment">     * 递归实现二分查找</span></span><br><span class="line"><span class="comment">     * <span class="doctag">@param</span> target</span></span><br><span class="line"><span class="comment">     * <span class="doctag">@return</span></span></span><br><span class="line"><span class="comment">     */</span></span><br><span class="line">    <span class="keyword">public</span> <span class="type">int</span> <span class="title function_">searchRecursion</span><span class="params">(<span class="type">int</span> target)</span> &#123;</span><br><span class="line">        <span class="keyword">if</span> (array != <span class="literal">null</span>) &#123;</span><br><span class="line">            <span class="keyword">return</span> searchRecursion(target, <span class="number">0</span>, array.length - <span class="number">1</span>);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">private</span> <span class="type">int</span> <span class="title function_">searchRecursion</span><span class="params">(<span class="type">int</span> target, <span class="type">int</span> start, <span class="type">int</span> end)</span> &#123;</span><br><span class="line">        <span class="keyword">if</span> (start &gt; end) &#123;</span><br><span class="line">            <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="type">int</span> <span class="variable">mid</span> <span class="operator">=</span> start + (end - start) / <span class="number">2</span>;</span><br><span class="line">        <span class="keyword">if</span> (array[mid] == target) &#123;</span><br><span class="line">            <span class="keyword">return</span> mid;</span><br><span class="line">        &#125; <span class="keyword">else</span> <span class="keyword">if</span> (target &lt; array[mid]) &#123;</span><br><span class="line">            <span class="keyword">return</span> searchRecursion(target, start, mid - <span class="number">1</span>);</span><br><span class="line">        &#125; <span class="keyword">else</span> &#123;</span><br><span class="line">            <span class="keyword">return</span> searchRecursion(target, mid + <span class="number">1</span>, end);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h4 id="二分查找的优化"><a href="#二分查找的优化" class="headerlink" title="二分查找的优化"></a>二分查找的优化</h4><p>为了找到 key 值所在的相对位置，让 key 的值更接近划分的位置，从而减少比较的次数。</p>
<p>这种二分查找的优化有个名字，叫插值查找，插值查找对于数列比较大并且比较均匀的数列来说，性能会好很多；但是如果数列极不均匀，则插值查找未必会比二分查找的性能好。</p>
<h4 id="二分查找的适用场景"><a href="#二分查找的适用场景" class="headerlink" title="二分查找的适用场景"></a>二分查找的适用场景</h4><p>二分查找要求数列本身有序，所以在选择的时候需要确认数列是否本身有序，如果无序，则还需要进行排序，确认这样的代价是否符合实际需求。</p>
<p>其实我们在获取一个列表的很多时候，可以直接使用数据库针对某个字段进行排序，在程序中需要找出某个值的元素时，就很适合使用二分查找了。</p>
<p>二分查找适合元素稍微多一些的数列，如果元素只有十几或者几十个，则其实可以直接使用顺序查找。</p>
<p>一般对一个有序列表，如果只需要对其进行一次排序，之后不再变化或者很少变化，则每次进行二分查找的效率就会很高；但是如果在一个有序列表中频繁地插入、删除数据，那么维护这个有序数列就会感觉很累。</p>
<h4 id="在数据结构中-非递减排序-的意思"><a href="#在数据结构中-非递减排序-的意思" class="headerlink" title="在数据结构中 非递减排序 的意思"></a>在数据结构中 <code>非递减排序</code> 的意思</h4><p>一个栗子：</p>
<figure class="highlight text"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line">1,2,3,4,5,........ : 递增排列</span><br><span class="line">9,8,7,6,5......... : 递减排列</span><br><span class="line">1，2，3，3，4，5，8，8，.............. : 非递减排列</span><br><span class="line">9，8，7，7，6，5，5，2，1，........ : 非递增排列</span><br></pre></td></tr></table></figure>

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